Approximate Vanishing Ideal via Data Knotting

The vanishing ideal is a set of polynomials that takes zero value on the given data points. Originally proposed in computer algebra, the vanishing ideal has been recently exploited for extracting the nonlinear structures of data in many applications. To avoid overfitting to noisy data, the polynomials are often designed to approximately rather than exactly equal zero on the designated data. Although such approximations empirically demonstrate high performance, the sound algebraic structure of the vanishing ideal is lost. The present paper proposes a vanishing ideal that is tolerant to noisy data and also pursued to have a better algebraic structure. As a new problem, we simultaneously find a set of polynomials and data points for which the polynomials approximately vanish on the input data points, and almost exactly vanish on the discovered data points. In experimental classification tests, our method discovered much fewer and lower-degree polynomials than an existing state-of-the-art method. Consequently, our method accelerated the runtime of the classification tasks without degrading the classification accuracy.Comment: 11 pages; AAAI'1

THE CRITICAL ROLE OF UNIVERSITIES IN IMPACTING UPON ENGLISH EDUCATION IN JAPAN

Learning a foreign education is compulsory in the Japanese primary and secondary school curricula, with most schools selecting English as their foreign language. Japan’s MEXT (Ministry of Education, Culture, Sports, Science and Technology) clearly identifies one of the main aims in teaching foreign languages is to improve students’ ability to communicate in the target language. However, many students in Japan continue to think of themselves as having only limited oral English communication skills, and are not confident when interacting orally. The majority of Japanese students are primarily externally-motivated English learners: they study simply to pass examinations. Thus students’ motivation for studying English isinconsistent with the Ministry’s aim in teaching it. Despite this, the current lack of opportunity for students to practise their English communication skills could be overcome by implementing systematic plans and achievable strategies. To enable the provision of such opportunities, the role of Japan’s higher education institutions, including universities, must be reassessed. This paper sets out ways in which universities can play a critical role in promoting practical strategies for improving and positively influencing students’ practical English skills in primary and secondary schools. The paper discusses three key suggestions for improving the use of English as an oral communication tool: (1) the inclusion of oral performance in English in the university entrance examination, (2) the development of coherent learning processes for achieving specified outcomes at the university level, and (3) the introduction of teacher-training opportunities for current university lecturers of English

Gradient Boosts the Approximate Vanishing Ideal

In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data approximately lie. In particular, the basis construction algorithms developed in machine learning are widely used in applications across many fields because of their monomial-order-free property; however, they lose many of the theoretical properties of computer-algebraic algorithms. In this paper, we propose general methods that equip monomial-order-free algorithms with several advantageous theoretical properties. Specifically, we exploit the gradient to (i) sidestep the spurious vanishing problem in polynomial time to remove symbolically trivial redundant bases, (ii) achieve consistent output with respect to the translation and scaling of input, and (iii) remove nontrivially redundant bases. The proposed methods work in a fully numerical manner, whereas existing algorithms require the awkward monomial order or exponentially costly (and mostly symbolic) computation to realize properties (i) and (iii). To our knowledge, property (ii) has not been achieved by any existing basis construction algorithm of the approximate vanishing ideal.Comment: 9+10 pages, 1+4 figures, AAAI'2

Movement of Calcuium (45Ca) to Fruit from Peduncle of Tomato Plants

Movement of calcium (45Ca) from the peduncle to fruit of tomato during the days and night was investigated. Further, the effects of additional NaCl to the culture solution on the water potential in plants and 45Ca movement to fruit were also examined. The activity of 45Ca on a dry weight basis in the peduncle was higher during the day than at night, however, in calyx and fruit the 45Ca activity was similar both during the day and night. Import of 45Ca into the leaves from the peduncle was not different between the day and the night. Additional NaCl to the culture solution resulted in a greater water saturation deficit (WSD) of the immature leaves just below the 2nd and 3rd trusses, unlike with the mature leaves below the 1st truss where the WSD did not decrease with NaCl treatment. On the oher hand, the activity of 45Ca in the peduncle and calyx was not different between the NaCl treatment and the control. However, the activity in the distal part of the fruits was lower with, NaCl treament than in the control. These results suggested that the high WSD effectively decreased the import of calcium into fruits from the peduncle. It seems that the import of 45Ca into fruit not only dependent on the conductive tissues but also a possible driving force in xylem water flow, and that NaCl interferes with movement of calcium in the fruits.トマト果柄に木綿糸を通してカルシウム(45Ca)を処理し昼夜間別に果房各部位への45Caの移行、ならびに、培養液にNaClを添加した場合の樹体内の水分状態と果実への45Ca移行について調査した。昼夜間における単位乾物重当りの45Caの非活性は果柄で昼間に有意に高くなったが、がく・果実では昼夜間差は生じなかった。また、葉でも昼夜間差はなく昼夜同程度に45Caの移行が認められた。培養液にNaClを添加しても、第1果房直下葉(成熟葉)の水分欠差が生じなかったが、第2･3段果房直下葉(未成熟葉)ではNaCl添加のよって水分欠差は有意に増大し、果柄・がくの45Ca非活性も高くなる傾向を示した。しかし果実末端部の45Ca非活性は有意に低くなり、同時に、果実全体に占める果実末端部での45Ca非活性もNaCl添加によって減少した。本試験の結果から、木綿糸処理液の果柄内への流入は樹体の水分欠差に影響を受けると考えられた。果柄内に流入した45Caは、水の流れだけでなく他の要因によっても各部位に移行するものと思われた。また、培養液へのNaCl添加により、果実末端部へのカルシウム移行がより強く抑制されるのは、果実内でのカチオン移動に競合が生じるからではないかと推察された